Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

doi:10.1007/s11709-022-0900-7

Front. Struct. Civ. Eng.

2022, Vol. 16

Issue (12) : 1530-1551 https://doi.org/10.1007/s11709-022-0900-7

RESEARCH ARTICLE

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

Yeong-Bin Yang^1,^2,³, Zeyang Zhou¹(

), Xiongfei Zhang¹, Xiaoli Wang¹

¹. School of Civil Engineering, Chongqing University, Chongqing 400045, China
². MOE Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing 400045, China
³. School of Civil Engineering and Architecture, Chongqing University of Science and Technology, Chongqing 400045, China

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Abstract

The seismic analysis of a viscoelastic half-space under two-dimensional (2D) oblique incident waves is carried out by the finite/infinite element method (FIEM). First, the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves. With the present formulation, no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear, while no critical angle exists for P waves. Next, the equivalent seismic forces of the earthquake (Taft Earthquake 1952) imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum. Based on the asymmetric finite/infinite element model, the frequency-domain motion equations for seismic analysis are presented with the key parameters selected. The results obtained in frequency and time domain are verified against those of Wolf’s, Luco and de Barros’ and for inversely computed ground motions. The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles, but not for under-critical incident angles. Other observations were also made for the numerical results inside the text.

Keywords oblique incident waves critical angle half-space finite/infinite element approach seismic response analysis

Corresponding Author(s): Zeyang Zhou

Just Accepted Date: 24 October 2022 Online First Date: 27 December 2022 Issue Date: 16 January 2023

Cite this article:

Yeong-Bin Yang,Zeyang Zhou,Xiongfei Zhang, et al. Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method[J]. Front. Struct. Civ. Eng., 2022, 16(12): 1530-1551.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0900-7
https://academic.hep.com.cn/fsce/EN/Y2022/V16/I12/1530

Fig.1 A half-space under oblique incident seismic waves.

Fig.2 Free surface subjected to oblique incident P waves.

Fig.3 Free surface subjected to oblique incident SV waves.

Fig.4 Free surface subjected to SV waves with incident angles over the critical angle.

Fig.5 Boundaries of near field in rectangular form subjected to oblique incident seismic waves.

Fig.6 Wave field on near-field boundary for oblique incident seismic waves.

Fig.7 Acceleration histories of Taft Earthquake: (a) horizontal; (b) vertical.

Fig.8 Acceleration frequency spectra of Taft Earthquake: (a) horizontal; (b) vertical.

Fig.9 Finite/infinite element mesh.

Fig.10 Q5 infinite element: (a) global coordinates; (b) local coordinates.

Fig.11 Selection of wave numbers for: (a) incident P waves and SV waves with incident angles below the critical angle; (b) SV waves with incident angles over the critical angle.

Fig.12 Normalized ground displacement amplitudes subjected to incident P waves: (a) horizontal; (b) vertical.

Fig.13 Normalized ground displacement amplitudes subjected to incident SV waves: (a) horizontal; (b) vertical.

Fig.14 Half-space containing a cylindrical cavity.

Fig.15 Normalized ground displacement amplitudes of the half-space containing a cylindrical cavity under P-wave incidence: (a) horizontal; (b) vertical.

Fig.16 Normalized ground displacement amplitudes of the half-space containing a cylindrical cavity under SV-waves: (a) horizontal; (b) vertical.

Fig.17 Ground acceleration time histories of point OP-1: (a) horizontal (SV waves); (b) vertical (P waves).

Fig.18 Normalized displacement amplitudes on free surface subjected to oblique incident P waves: (a) horizontal; (b) vertical.

Fig.19 Normalized displacement amplitudes on vertical central line subjected to oblique incident P waves: (a) horizontal; (b) vertical.

Fig.20 Normalized displacement amplitudes on vertical central line subjected to P waves with different incident angles: (a) horizontal; (b) vertical.

Fig.21 Normalized horizontal and vertical displacement amplitudes subjected to oblique incident P waves along: (a) x-axis; (b) y-axis.

Fig.22 Normalized displacement amplitudes on free surface subjected to oblique incident SV waves: (a) horizontal; (b) vertical.

Fig.23 Normalized displacement amplitudes on vertical central line subjected to oblique incident SV waves: (a) horizontal; (b) vertical.

Fig.24 Normalized displacement amplitudes on vertical central line subjected to SV waves with different incident angles: (a) horizontal; (b) vertical.

Fig.25 Normalized horizontal and vertical displacement amplitudes subjected to oblique incident SV waves along: (a) x-axis; (b) y-axis.

Fig.26 Horizontal acceleration time histories on free surface subjected to P waves with incident angle of: (a) 15°; (b) 50°; (c) 85°.

Fig.27 Vertical acceleration time histories on free surface subjected to P waves with incident angle of: (a) 15°; (b) 50°; (c) 85°.

Fig.28 Maximum values of horizontal acceleration time histories subjected to P waves with different incident angles on: (a) free surface; (b) vertical central line.

Fig.29 Maximum values of horizontal and vertical acceleration time histories subjected to oblique incident P waves along: (a) x-axis; (b) y-axis.

Fig.30 Horizontal acceleration time histories on free surface subjected to SV waves with incident angle of: (a) 15°; (b) 50°; (c) 85°.

Fig.31 Vertical acceleration time histories on free surface subjected to SV waves with incident angle of: (a) 15°; (b) 50°; (c) 85°.

Fig.32 Maximum values of vertical acceleration time histories subjected to SV waves with different incident angles on: (a) free surface; (b) vertical central line.

Fig.33 Maximum values of horizontal and vertical acceleration time histories subjected to oblique incident SV waves along: (a) x-axis; (b) y-axis.

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